Die Entwicklung der Mesofauna eines Weinberges im nordöstlichen Rheinhessen im Vergleich zum Lennebergwald und weiteren Agrarflächen

ZusammenfassungrnrnrnDer Köderstreifentest, die Auswertung der Minicontainer und die Erfassung der Bodenlebewesen mit Hilfe der Bodenstechkerne ergeben zusammen eine gut standardisierte Methode zur Darstellung und Beurteilung der Mesofauna. Unter der Vorraussetzung gleicher abiotischer Faktoren ist es problemlos möglich, selbst unterschiedliche Standorte wie Agrarflächen, Weinberge und Waldböden vergleichend zu untersuchen.rnrnAuf den verschiedenen Versuchsflächen des Laubenheimer Weinberges gelingt es deutlich zu zeigen, wie wichtig eine naturnahe Begrünung für den Boden ist. Dies betrifft nicht nur die Entwicklung der Humusschicht und damit die Bodenlebewesen, sondern auch die Schaffung von Kapillaren und Poren, die durch schwere landwirtschaftliche Geräte im Rahmen der Bo-denverdichtung reduziert werden. Erosionserscheinungen kommen vollständig zum Stillstand. Das Ökosystem Boden sollte auch so gut wie keine Belastung durch Herbizide, Insektizide und Pestizide erfahren. Ähnliches gilt auch für agrarisch genutzte Flächen. rnrnDer Lennebergwald als Naherholungsregion von Mainz ist besonders schützenswert, da dieser durch intensiven Immissionseintrag aufgrund der Nähe zu den Autobahnen und durch die Eutrophierung über die Haustiere stark belastet wird. Die immer größere Ausdehnung des Siedlungsgebietes und die damit verbundene steigende Anzahl an Waldbesuchern, die durch Verlassen der vorgegebenen Wege den Boden zerstören, gefährden zusätzlich das Ökosystem.rnrnÜber Sinn und Zweck einer Flurbereinigung zu diskutieren ist hier nicht angebracht. Aus bo-denkundlicher Sicht ist sie nicht zu befürworten, da hiermit alle bodenbewahrenden Maßnah-men ignoriert werden. Wichtig ist es, bei den Landwirten Aufklärungsarbeit zu leisten, was bodenschonende und bodenweiterentwickelnde Bearbeitungsmethoden bedeuten. Mit Hilfe sachgemäßer Aufklärung und richtiger Umsetzung kann durch Begrünungsmaßnahmen der zum Teil sehr stark strapazierte Boden erhalten, gefördert und auf lange Sicht stabilisiert wer-den.rnrnAufgrund der festgestellten Tatsachen wurde ab 2008 auf eine flächige Dauerbegrünung um-gestellt, so dass es auch in den unbegrünten Rebzeilen zu einer Bodenverbesserung kommen kann. Mit großer Wahrscheinlichkeit dürfte diese schneller voranschreiten, da die Mesofauna von den benachbarten begrünten Rebzeilen einwandern kann. rnDie Mesofauna landwirtschaftlich genutzter Flächen und Waldgebiete kann, obwohl extrem unterschiedlich, miteinander verglichen werden.rnrnBrachflächen und Waldgebiete lassen sich aufgrund der unberührten Bodenstrukturen sogar gut miteinander vergleichen. Temperatur- und Niederschlagsverhältnisse müssen dabei über-einstimmen. Die Azidität der jeweiligen Böden gilt es zu berücksichtigen, da verschiedene Tiergruppen damit unterschiedlich umgehen. Collembolen bevorzugen neutrale Böden, wäh-rend Acari als Räuber mit den Lebewesen in sauren Böden besser zurechtkommen. Die Streu-auflage ist dabei von großer Bedeutung.rnrnIm Rahmen von Bearbeitungsmaßnahmen kommt es durch jeglichen Maschineneinsatz zu ei-ner mehr oder weniger starken Veränderung der Bodenstruktur und somit auch der darin le-benden Mesofauna. Bis sich diese erholt hat, steht meist schon die nächste Bodenbewirtschaf-tung an. Die Bodenverdichtung spielt auch eine Rolle. Bei herkömmlichem Ackerbau ist eine Fruchtfolge mit eingeschalteter Brache oder Gründüngung mit Klee oder Luzerne angebracht, um die Mesofauna nicht zu stark zu strapazieren. Organische Düngegaben leicht abbaubarer Streu sind deutlich zu bevorzugen gegenüber sehr zellulose- und ligninhaltigen Pflanzenresten. Die Einbringung von Stoppeln nach Aberntung von Getreidefeldern ist sinnvoll, solange dabei nicht zu tief in die Bodenstruktur eingegriffen wird (ZIMMER 1997).rnrnIm Rahmen der Sonderkultur Wein, bei der eine Bodenbearbeitung aus den aufgezeigten Gründen eigentlich nicht notwendig wäre, sind Dauerbegrünungsmaßnahmen generell von Nutzen: der Erosion wird vorgebeugt, die Bodenfeuchte konstant gehalten, der anfallende Mulch als Gründüngung genutzt. Dies sind alles entscheidende Faktoren, die die Meso- und Makrofauna fördern. Nur die Bodenverdichtung durch schweres Gerät, wie Schlepper und Vollernter, sind für den Boden nicht förderlich (HEISLER 1993, EHRENSBERGER 1993). Nie-derdruckreifen und Verringerung der Befahrung sind geeignete Gegenmaßnahmen. rnrnEntgegen landläufiger Winzermeinung, stellen die Pflanzen einer Begrünung eigentlich keine Konkurrenz für die Weinstöcke dar. Die Vorteile einer Begrünung sind nicht nur die Förde-rung der einheimischen Flora in ihrem standortgerechten Artenreichtum, sondern auch Ver-vielfältigung von Meso- und Makrofauna aufgrund der dadurch mehr anfallenden und ein-zuarbeitenden leicht abbaubaren Streu (GRIEBEL 1995).rn

Multilevel Domain Decomposition Algorithms for Monolithic Fluid-Structure Interaction Problems with Application to Haemodynamics

Finite element techniques for solving the problem of fluid-structure interaction of an elastic solid material in a laminar incompressible viscous flow are described. The mathematical problem consists of the Navier-Stokes equations in the Arbitrary Lagrangian-Eulerian formulation coupled with a non-linear structure model, considering the problem as one continuum. The coupling between the structure and the fluid is enforced inside a monolithic framework which computes simultaneously for the fluid and the structure unknowns within a unique solver. We used the well-known Crouzeix-Raviart finite element pair for discretization in space and the method of lines for discretization in time. A stability result using the Backward-Euler time-stepping scheme for both fluid and solid part and the finite element method for the space discretization has been proved. The resulting linear system has been solved by multilevel domain decomposition techniques. Our strategy is to solve several local subproblems over subdomain patches using the Schur-complement or GMRES smoother within a multigrid iterative solver. For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a set of two FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in a laminar channel flow, allowing stationary as well as periodically oscillating deformations, and for a benchmark proposed by COMSOL multiphysics where a narrow vertical structure attached to the bottom wall of a channel bends under the force due to both viscous drag and pressure. Then, as an example of fluid-structure interaction in biomedical problems, we considered the academic numerical test which consists in simulating the pressure wave propagation through a straight compliant vessel. All the tests show the applicability and the numerical efficiency of our approach to both two-dimensional and three-dimensional problems.

Valutazione della mobilita' di contaminanti inorganici tramite test di cessione su matrici ambientali contaminate

La caratterizzazione di sedimenti contaminati è un problema complesso, in questo lavoro ci si è occupati di individuare una metodologia di caratterizzazione che tenesse conto sia delle caratteristiche della contaminazione, con analisi volte a determinare il contenuto totale di contaminanti, sia della mobilità degli inquinanti stessi. Una adeguata strategia di caratterizzazione può essere applicata per la valutazione di trattamenti di bonifica, a questo scopo si è valutato il trattamento di soil washing, andando ad indagare le caratteristiche dei sedimenti dragati e del materiale in uscita dal processo, sabbie e frazione fine, andando inoltre a confrontare le caratteristiche della sabbia in uscita con quelle delle sabbie comunemente usate per diverse applicazioni. Si è ritenuto necessario indagare la compatibilità dal punto di vista chimico, granulometrico e morfologico. Per indagare la mobilità si è scelto di applicare i test di cessione definiti sia a livello internazionale che italiano (UNI) e quindi si sono sviluppate le tecnologie necessarie alla effettuazione di test di cessione in modo efficace, automatizzando la gestione del test a pHstat UNI CEN 14997. Questo si è reso necessario a causa della difficoltà di gestire il test manualmente, per via delle tempistiche difficilmente attuabili da parte di un operatore. Le condizioni redox influenzano la mobilità degli inquinanti, in particolare l’invecchiamento all’aria di sedimenti anossici provoca variazioni sensibili nello stato d’ossidazione di alcune componenti, incrementandone la mobilità, si tratta quindi di un aspetto da considerare quando si individuano le adeguate condizioni di stoccaggio-smaltimento, si è eseguita a questo scopo una campagna sperimentale.

Interference Management and Energy Efficiency in Satellite Communications

The main areas of research of this thesis are Interference Management and Link-Level Power Efficiency for Satellite Communications. The thesis is divided in two parts. Part I tackles the problem of interference environments in satellite communications, and interference mitigation strategies, not just in terms of avoidance of the interferers, but also in terms of actually exploiting the interference present in the system as a useful signal. The analysis follows a top-down approach across different levels of investigation, starting from system level consideration on interference management, down to link-level aspects and to intra-receiver design. Interference Management techniques are proposed at all the levels of investigation, with interesting results. Part II is related to efficiency in the power domain, for instance in terms of required Input Back-off at the power amplifiers, which can be an issue for waveform based on linear modulations, due to their varying envelope. To cope with such aspects, an analysis is carried out to compare linear modulation with waveforms based on constant envelope modulations. It is shown that in some scenarios, constant envelope waveforms, even if at lower spectral efficiency, outperform linear modulation waveform in terms of energy efficiency.

On the car sequencing problem: analysis and solution methods

This work deals with the car sequencing (CS) problem, a combinatorial optimization problem for sequencing mixed-model assembly lines. The aim is to find a production sequence for different variants of a common base product, such that work overload of the respective line operators is avoided or minimized. The variants are distinguished by certain options (e.g., sun roof yes/no) and, therefore, require different processing times at the stations of the line. CS introduces a so-called sequencing rule H:N for each option, which restricts the occurrence of this option to at most H in any N consecutive variants. It seeks for a sequence that leads to no or a minimum number of sequencing rule violations. In this work, CS’ suitability for workload-oriented sequencing is analyzed. Therefore, its solution quality is compared in experiments to the related mixed-model sequencing problem. A new sequencing rule generation approach as well as a new lower bound for the problem are presented. Different exact and heuristic solution methods for CS are developed and their efficiency is shown in experiments. Furthermore, CS is adjusted and applied to a resequencing problem with pull-off tables.

Technology Development and Consumer Acceptance of Innovation in Fruit Production

Precision Agriculture (PA) and the more specific branch of Precision Horticulture are two very promising sectors. They focus on the use of technologies in agriculture to optimize the use of inputs, so to reach a better efficiency, and minimize waste of resources. This important objective motivated many researchers and companies to search new technology solutions. Sometimes the effort proved to be a good seed, but sometimes an unfeasible idea. So that PA, from its birth more or less 25 years ago, is still a “new” management, interesting for the future, but an actual low adoption rate is still reported by experts and researchers. This work aims to give a contribution in finding the causes of this low adoption rate and proposing a methodological solution to this problem. The first step was to examine prior research about Precision Agriculture adoption, by ex ante and ex post approach. It was supposed as important to find connections between these two phases of a purchase experience. In fact, the ex ante studies dealt with potential consumer’s perceptions before a usage experience occurred, therefore before purchasing a technology, while the ex post studies described the drivers which made a farmer become an end-user of PA technology. Then, an example of consumer research is presented. This was an ex ante research focused on pre-prototype technology for fruit production. This kind of research could give precious information about consumer acceptance before reaching an advanced development phase of the technology, and so to have the possibility to change something with the least financial impact. The final step was to develop the pre-prototype technology that was the subject of the consumer acceptance research and test its technical characteristics.

Evaluation of the photosynthetic efficiency of sweet sorghum under drought and cold conditions

Sweet sorghum, a C4 crop of tropical origin, is gaining momentum as a multipurpose feedstock to tackle the growing environmental, food and energy security demands. Under temperate climates sweet sorghum is considered as a potential bioethanol feedstock, however, being a relatively new crop in such areas its physiological and metabolic adaptability has to be evaluated; especially to the more frequent and severe drought spells occurring throughout the growing season and to the cold temperatures during the establishment period of the crop. The objective of this thesis was to evaluate some adaptive photosynthetic traits of sweet sorghum to drought and cold stress, both under field and controlled conditions. To meet such goal, a series of experiments were carried out. A new cold-tolerant sweet sorghum genotype was sown in rhizotrons of 1 m3 in order to evaluate its tolerance to progressive drought until plant death at young and mature stages. Young plants were able to retain high photosynthetic rate for 10 days longer than mature plants. Such response was associated to the efficient PSII down-regulation capacity mediated by light energy dissipation, closure of reaction centers (JIP-test parameters), and accumulation of glucose and sucrose. On the other hand, when sweet sorghum plants went into blooming stage, neither energy dissipation nor sugar accumulation counteracted the negative effect of drought. Two hybrids with contrastable cold tolerance, selected from an early sowing field trial were subjected to chilling temperatures under controlled growth conditions to evaluate in deep their physiological and metabolic cold adaptation mechanisms. The hybrid which poorly performed under field conditions (ICSSH31), showed earlier metabolic changes (Chl a + b, xanthophyll cycle) and greater inhibition of enzymatic activity (Rubisco and PEPcase activity) than the cold tolerant hybrid (Bulldozer). Important insights on the potential adaptability of sweet sorghum to temperate climates are given.

Untersuchungen zur Genauigkeit adaptiver unstetiger Galerkin-Simulationen mit Hilfe von Luftblasen-Testfällen

Allgemein erlaubt adaptive Gitterverfeinerung eine Steigerung der Effizienz numerischer Simulationen ohne dabei die Genauigkeit des Ergebnisses signifikant zu verschlechtern. Es ist jedoch noch nicht erforscht, in welchen Bereichen des Rechengebietes die räumliche Auflösung tatsächlich vergröbert werden kann, ohne die Genauigkeit des Ergebnisses signifikant zu beeinflussen. Diese Frage wird hier für ein konkretes Beispiel von trockener atmosphärischer Konvektion untersucht, nämlich der Simulation von warmen Luftblasen. Zu diesem Zweck wird ein neuartiges numerisches Modell entwickelt, das auf diese spezielle Anwendung ausgerichtet ist. Die kompressiblen Euler-Gleichungen werden mit einer unstetigen Galerkin Methode gelöst. Die Zeitintegration geschieht mit einer semi-implizite Methode und die dynamische Adaptivität verwendet raumfüllende Kurven mit Hilfe der Funktionsbibliothek AMATOS. Das numerische Modell wird validiert mit Hilfe einer Konvergenzstudie und fünf Standard-Testfällen. Eine Methode zum Vergleich der Genauigkeit von Simulationen mit verschiedenen Verfeinerungsgebieten wird eingeführt, die ohne das Vorhandensein einer exakten Lösung auskommt. Im Wesentlichen geschieht dies durch den Vergleich von Eigenschaften der Lösung, die stark von der verwendeten räumlichen Auflösung abhängen. Im Fall einer aufsteigenden Warmluftblase ist der zusätzliche numerische Fehler durch die Verwendung der Adaptivität kleiner als 1% des gesamten numerischen Fehlers, wenn die adaptive Simulation mehr als 50% der Elemente einer uniformen hoch-aufgelösten Simulation verwendet. Entsprechend ist die adaptive Simulation fast doppelt so schnell wie die uniforme Simulation.

Experiments on Pro-Sociality and Environmental Issues

The thesis comprises three essays that use experimental methods, one about other-regarding motivations in economic behavior and the others on pro-social behavior in two environmental economics problems. The first chapter studies how the expectations of the others and the concern to maintain a balance between effort exerted and rewards obtained interact in shaping the behavior in a modified dictator game. We find that dictators condition their choices on recipients' expectations only when there is a high probability that the the recipient will not be compensated for her effort. Otherwise, dictators tend to balance the efforts and rewards of the recipients, irrespective of the recipients' expectations. In the second chapter, I investigate the problem of local opposition to large public projects (e.g. landfills, incinerators, etc.). In particular, the experiment shows how the uncertainty about the project's quality makes the community living in the host site skeptical about the project. I also test whether side-transfers and costly information disclosure can help to increase the efficiency. Both tools succesfully make the host more willing to accept the project, but they lead to the realization of different types of projects. The last chapter is an experiment on climate negotiations. To avoid the global warming, countries are called to cooperate in the abatement of their emissions. We study whether the dynamic aspect of the climate change makes cooperation across countries behaviorally more difficult. We also consider inequality across countries as a possible factor that hinders international cooperation.

Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

Energy-efficient Communication and Estimation in Wireless Sensor Networks

This thesis focuses on the energy efficiency in wireless networks under the transmission and information diffusion points of view. In particular, on one hand, the communication efficiency is investigated, attempting to reduce the consumption during transmissions, while on the other hand the energy efficiency of the procedures required to distribute the information among wireless nodes in complex networks is taken into account. For what concerns energy efficient communications, an innovative transmission scheme reusing source of opportunity signals is introduced. This kind of signals has never been previously studied in literature for communication purposes. The scope is to provide a way for transmitting information with energy consumption close to zero. On the theoretical side, starting from a general communication channel model subject to a limited input amplitude, the theme of low power transmission signals is tackled under the perspective of stating sufficient conditions for the capacity achieving input distribution to be discrete. Finally, the focus is shifted towards the design of energy efficient algorithms for the diffusion of information. In particular, the endeavours are aimed at solving an estimation problem distributed over a wireless sensor network. The proposed solutions are deeply analyzed both to ensure their energy efficiency and to guarantee their robustness against losses during the diffusion of information (against information diffusion truncation more in general).

Test sperimentali e modellazione di una torre di lavaggio per la filtrazione di particolato sottile in impianti di combustione delle biomasse

This study investigates biomass and particulate matter also known as PM produced from the combustion of a domestic boiler powered by mais and how to separate PM from the stream of smoke output from the boiler using wet scrubber with structured packing. Sperimentations show the inefficiency of the separator used, so we provide an optimization of the structured packing changing geometric parameters as angle of the bend or thickness of the channels. In order to obtain a higher separation efficiency we remove the structured packinkg and introduce a packed bed composed of spheres of polyethylene with a diameter of 3 mm.

Regularization methods for the solution of a nonlinear least-squares problem in tomography

In this work we study a polyenergetic and multimaterial model for the breast image reconstruction in Digital Tomosynthesis, taking into consideration the variety of the materials forming the object and the polyenergetic nature of the X-rays beam. The modelling of the problem leads to the resolution of a high-dimensional nonlinear least-squares problem that, due to its nature of inverse ill-posed problem, needs some kind of regularization. We test two main classes of methods: the Levenberg-Marquardt method (together with the Conjugate Gradient method for the computation of the descent direction) and two limited-memory BFGS-like methods (L-BFGS). We perform some experiments for different values of the regularization parameter (constant or varying at each iteration), tolerances and stop conditions. Finally, we analyse the performance of the several methods comparing relative errors, iterations number, times and the qualities of the reconstructed images.

L'algoritmo bionomico per il Traveling Salesman Problem

In questa tesi viene presentato un nuovo metaeuristico per la risoluzione del Traveling Salesman Problem (TSP) simmetrico. Tale metodo, detto algoritmo bionomico, è una variante dell'algoritmo genetico che usa un metodo innovativo di generazione del parents set. Nella tesi vengono proposti diversi metodi di crossover specifici per il TSP ma che possono essere facilmente estesi per altri problemi di ottimizzazione combinatoria. Tali metodi sono stati sperimentati su un insieme di problemi test, i risultati computazionali mostrano l'efficienza dei metodi proposti. In particolare uno dei metodi domina gli altri sia per la miglior qualità delle soluzioni prodotte che per il minor tempo di calcolo impiegato.

Efficiency limits for silicon/perovskite tandem solar cells: a theoretical model

The primary goal of this work is related to the extension of an analytic electro-optical model. It will be used to describe single-junction crystalline silicon solar cells and a silicon/perovskite tandem solar cell in the presence of light-trapping in order to calculate efficiency limits for such a device. In particular, our tandem system is composed by crystalline silicon and a perovskite structure material: metilammoniumleadtriiodide (MALI). Perovskite are among the most convenient materials for photovoltaics thanks to their reduced cost and increasing efficiencies. Solar cell efficiencies of devices using these materials increased from 3.8% in 2009 to a certified 20.1% in 2014 making this the fastest-advancing solar technology to date. Moreover, texturization increases the amount of light which can be absorbed through an active layer. Using Green’s formalism it is possible to calculate the photogeneration rate of a single-layer structure with Lambertian light trapping analytically. In this work we go further: we study the optical coupling between the two cells in our tandem system in order to calculate the photogeneration rate of the whole structure. We also model the electronic part of such a device by considering the perovskite top cell as an ideal diode and solving the drift-diffusion equation with appropriate boundary conditions for the silicon bottom cell. We have a four terminal structure, so our tandem system is totally unconstrained. Then we calculate the efficiency limits of our tandem including several recombination mechanisms such as Auger, SRH and surface recombination. We focus also on the dependence of the results on the band gap of the perovskite and we calculare an optimal band gap to optimize the tandem efficiency. The whole work has been continuously supported by a numerical validation of out analytic model against Silvaco ATLAS which solves drift-diffusion equations using a finite elements method. Our goal is to develop a simpler and cheaper, but accurate model to study such devices.